We obtain a solution to a zone-centered discretization of the one dimensional time-dependent diffusion equation with arbitrary initial conditions and source, constant absorption and scattering opacity, and constant zone size and time step. The solution is obtained using the discrete Green’s functions of the discretized equation. The solution of the discretized equation is useful in the testing of computer codes, because the code can be expected to agree with the solution to the discrete equation, to within small errors caused by roundoff. This is in contrast to solutions of the differential equation, with which the code results only approximately agree. The usefulness of the solution for tests of an inertial confinement fusion code is demonstrated.

我们获得一维时变扩散方程的区域中心离散化的解决方案，该方程具有任意初始条件和源，恒定的吸收和散射不透明度以及恒定的区域大小和时间步长。使用离散方程的离散格林函数获得解。离散方程的解在计算机代码的测试中很有用，因为可以期望该代码与离散方程的解一致，并且在舍入引起的小误差内。这与微分方程的解相反，后者的代码结果仅近似一致。证明了该解决方案对于惯性约束融合码测试的有用性。